Quantum states with a space-like energy momentum

TL;DR

This paper demonstrates that in a Dirac-Maxwell quantum field, certain states can have spacelike energy-momentum, challenging the common assumption that all quantum states must have timelike energy-momentum, and implying the existence of states with less energy than the vacuum.

Contribution

It proves the existence of quantum states with spacelike energy-momentum in a Dirac-Maxwell field, contradicting the usual timelike assumption in quantum field theory.

Findings

Existence of spacelike energy-momentum states in Dirac-Maxwell fields

Quantum states with less energy than the vacuum state

Challenges the standard assumption in quantum field theory

Abstract

A common assumption in quantum field theory is that the energy-momentum 4-vector of any quantum state must be timelike. It will be proven that this is not the case for a Dirac-Maxwell field. In this case quantum states can be shown to exist whose energy-momentum is spacelike. This implies that there must exist quantum states with less energy than the vacuum state.